A cantilever beam has a concentrated load, and then the beam vibration critically damps. Lobatto integration rules place the quadrature points on the true surfaces of the shell. [See Hughes].

*INTEGRATION_SHELL Cantilever Beam with Lobatto Integration LS-DYNA Manual Section: *INTEGRATION_SHELL Additional Sections: *DAMPING_GLOBAL *LOAD_NODE_POINT Example: Cantilever Beam with Lobatto Integration Filename: integration_shell.lobotto.beam.k Description: A cantilever beam has a concentrated load, and then the beam vibration critically damps. Lobatto integration rules place the quadrature points on the true surfaces of the shell. [See Hughes]. Model: The plate measures 1.00 * 0.10 * 0.01 in^3 and is modeled with 60 Belytschko-Tsay shell elements. The displacement of the nodes is fixed at one end and a concentrated load is applied to the other end. Symmetry conditions for the plane strain case exist on the beam sides. Input: The concentrated loads and load curve definition 1 defines the load on the end of the beam (*LOAD_NODE_POINT, *DEFINE_CURVE). The beam is critically damped (*DAMPING_GLOBAL) The number of integration points is 5 (*SECTION_SHELL). The shell integration rule is the Lobatto integration rule (*SECTION_SHELL) Results: The displacement of the beam damps out critically. The x-stress values at the integration points exhibit tension on one side, compression on the opposite side, and balance at the neutral axis.

*CONTROL_ENERGY *CONTROL_OUTPUT *CONTROL_TERMINATION *DAMPING_GLOBAL *DATABASE_BINARY_D3PLOT *DATABASE_BINARY_D3THDT *DATABASE_ELOUT *DATABASE_EXTENT_BINARY *DATABASE_GLSTAT *DATABASE_HISTORY_NODE *DATABASE_HISTORY_SHELL *DATABASE_NODOUT *DEFINE_CURVE *ELEMENT_SHELL *END *INTEGRATION_SHELL *KEYWORD *LOAD_NODE_POINT *MAT_PLASTIC_KINEMATIC *NODE *PART *SECTION_SHELL *TITLE

*KEYWORD *TITLE Lobatto Integration $ $ LSTC Example $ $ Last Modified: September 17, 1997 $ $ Units: lbf-s2/in, in, s, lbf, psi, lbf-in $ $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ $ $$$$ Control Ouput $ $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ $ $...>....1....>....2....>....3....>....4....>....5....>....6....>....7....>....8 $ *CONTROL_TERMINATION $ endtim endcyc dtmin endneg endmas 0.015 $ *CONTROL_ENERGY $ hgen rwen slnten rylen 2 $ *CONTROL_OUTPUT $ npopt neecho nrefup iaccop opifs ipnint ikedit 0 0 0 0 2 1000 $ $ *DATABASE_BINARY_D3PLOT $ dt lcdt 0.0003 $ *DATABASE_BINARY_D3THDT $ dt lcdt 10. $ *DATABASE_EXTENT_BINARY $ neiph neips maxint strflg sigflg epsflg rltflg engflg 5 $ cmpflg ieverp beamip $ *DATABASE_GLSTAT $ dt 0.0001 $ *DATABASE_ELOUT $ dt 0.0001 $ *DATABASE_HISTORY_SHELL $ id1 id2 id3 id4 id5 id6 id7 id8 1 $ *DATABASE_NODOUT $ dt 0.0001 $ *DATABASE_HISTORY_NODE $ id1 id2 id3 id4 id5 id6 id7 id8 31 $ $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ $ $$$$ Loading $ $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ $ $$$$ Load nodes 31, 62, 93 in the negative z-direction. $ $...>....1....>....2....>....3....>....4....>....5....>....6....>....7....>....8 $ *LOAD_NODE_POINT $ nid dof lcid sf cid m1 m2 m3 31 3 1 -1.00E+00 62 3 1 -1.00E+00 93 3 1 -1.00E+00 $ *DEFINE_CURVE $ lcid sidr scla sclo offa offo 1 $ a o 0.000E+00 0.000E+00 8.000E-03 1.667E-03 1.534E-02 1.667E-03 $ $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ $ $$$$ Damping $ $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ $ $...>....1....>....2....>....3....>....4....>....5....>....6....>....7....>....8 $ *DAMPING_GLOBAL $ lcid valdmp 2 0.0 $ *DEFINE_CURVE $ lcid sidr scla sclo offa offo 2 $ a o 0.000E+00 0.000E+00 8.000E-03 0.000E+00 1.000E-02 2.353E+03 1.534E-02 2.353E+03 $ $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ $ $$$$ Define Parts and Materials $ $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ $ $...>....1....>....2....>....3....>....4....>....5....>....6....>....7....>....8 $ *PART $ pid sid mid eosid hgid adpopt Cantilever Beam - Aluminum 1 1 1 $ $ *MAT_PLASTIC_KINEMATIC $ mid ro e pr sigy etan beta 1 7.85e-4 10.00e+6 0.300 20000.0 100000 1.0 $ src srp fs 0.0 0.0 0.0 $ $$$$ irid = -1 ===> integration rule 1 used (see below) $ *SECTION_SHELL $ sid elform shrf nip propt qr/irid icomp 1 0 5 -1 $ t1 t2 t3 t4 nloc 0.010 0.010 0.010 0.010 $ $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ $ $$$$ Integration Rule $ $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ $ $...>....1....>....2....>....3....>....4....>....5....>....6....>....7....>....8 $ *INTEGRATION_SHELL $ irid nip esop 1 5 $ s wf pid -1.000E+00 1.000E-01 -6.546E-01 5.444E-01 0.000E+00 7.111E-01 6.546E-01 5.444E-01 1.000E+00 1.000E-01 $ $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ $ $$$$ Define Nodes and Elements $ $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ $ $ *END